- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] a(c(d(x))) -> c(x)
[2] u(b(d(d(x)))) -> b(x)
[3] v(a(a(x))) -> u(v(x))
[4] v(a(c(x))) -> u(b(d(x)))
[5] v(c(x)) -> b(x)
[6] w(a(a(x))) -> u(w(x))
[7] w(a(c(x))) -> u(b(d(x)))
[8] w(c(x)) -> b(x)


Sub problem: 
guided: 

DP termination of:
<Marked_v(a(a(x))) , Marked_u(v(x))>
<Marked_v(a(a(x))) , Marked_v(x)>
<Marked_v(a(c(x))) , Marked_u(b(d(x)))>
<Marked_w(a(a(x))) , Marked_u(w(x))>
<Marked_w(a(a(x))) , Marked_w(x)>
<Marked_w(a(c(x))) , Marked_u(b(d(x)))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_v(a(a(x))) , Marked_v(x)> --> <Marked_v(a(a(x))) , Marked_v(x)>
}

{  <Marked_w(a(a(x))) , Marked_w(x)> --> <Marked_w(a(a(x))) , Marked_w(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a(c(d(x))) >= c(x) ;
  u(b(d(d(x)))) >= b(x) ;
  v(c(x)) >= b(x) ;
  v(a(c(x))) >= u(b(d(x))) ;
  v(a(a(x))) >= u(v(x)) ;
  w(c(x)) >= b(x) ;
  w(a(c(x))) >= u(b(d(x))) ;
  w(a(a(x))) >= u(w(x)) ;
  Marked_v(a(a(x))) >= Marked_v(x) ;
 }
 + Disjunctions:{ 
{
  Marked_v(a(a(x))) > Marked_v(x) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a(c(d(x))) >= c(x)
constraint: u(b(d(d(x)))) >= b(x)
constraint: v(c(x)) >= b(x)
constraint: v(a(c(x))) >= u(b(d(x)))
constraint: v(a(a(x))) >= u(v(x))
constraint: w(c(x)) >= b(x)
constraint: w(a(c(x))) >= u(b(d(x)))
constraint: w(a(a(x))) >= u(w(x))
constraint: Marked_v(a(a(x))) >= Marked_v(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a(c(d(x))) >= c(x) ;
  u(b(d(d(x)))) >= b(x) ;
  v(c(x)) >= b(x) ;
  v(a(c(x))) >= u(b(d(x))) ;
  v(a(a(x))) >= u(v(x)) ;
  w(c(x)) >= b(x) ;
  w(a(c(x))) >= u(b(d(x))) ;
  w(a(a(x))) >= u(w(x)) ;
  Marked_w(a(a(x))) >= Marked_w(x) ;
 }
 + Disjunctions:{ 
{
  Marked_w(a(a(x))) > Marked_w(x) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a(c(d(x))) >= c(x)
constraint: u(b(d(d(x)))) >= b(x)
constraint: v(c(x)) >= b(x)
constraint: v(a(c(x))) >= u(b(d(x)))
constraint: v(a(a(x))) >= u(v(x))
constraint: w(c(x)) >= b(x)
constraint: w(a(c(x))) >= u(b(d(x)))
constraint: w(a(a(x))) >= u(w(x))
constraint: Marked_w(a(a(x))) >= Marked_w(x)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a(c(d(x))) -> c(x)
[2] u(b(d(d(x)))) -> b(x)
[3] v(a(a(x))) -> u(v(x))
[4] v(a(c(x))) -> u(b(d(x)))
[5] v(c(x)) -> b(x)
[6] w(a(a(x))) -> u(w(x))
[7] w(a(c(x))) -> u(b(d(x)))
[8] w(c(x)) -> b(x)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_v(a(a(x))) , Marked_u(v(x))>
<Marked_v(a(a(x))) , Marked_v(x)>
<Marked_v(a(c(x))) , Marked_u(b(d(x)))>
<Marked_w(a(a(x))) , Marked_u(w(x))>
<Marked_w(a(a(x))) , Marked_w(x)>
<Marked_w(a(c(x))) , Marked_u(b(d(x)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_v(a(a(x))) , Marked_v(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ c ] (X0) = 0; 
 [ u ] (X0) = 2 + 3*X0 + 0; 
 [ d ] (X0) = 0; 
 [ w ] (X0) = 2*X0 + 0; 
 [ a ] (X0) = 1 + 2*X0 + 0; 
 [ Marked_v ] (X0) = 1*X0 + 0; 
 [ v ] (X0) = 2 + 2*X0 + 0; 
 [ b ] (X0) = 0; 
 ]} 
{
 
DP termination of:
<Marked_w(a(a(x))) , Marked_w(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ c ] (X0) = 0; 
 [ u ] (X0) = 1*X0 + 0; 
 [ d ] (X0) = 0; 
 [ w ] (X0) = 3 + 1*X0 + 0; 
 [ a ] (X0) = 1 + 2*X0 + 0; 
 [ v ] (X0) = 2 + 0; 
 [ b ] (X0) = 0; 
 [ Marked_w ] (X0) = 2*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.105286 seconds (real time)
Cime Exit Status: 0